In the present paper, a new neural network is developed to improve the prediction accuracy of crude oil price fluctuations. The proposed model combines wavelet neural network (WNN) with random time effective function. WNN is a predictive system with the ability to implement strong nonlinear approximation. The random time effective function is applied to formulate the varied impact of historical data on current market, which endows historical data with time-variant weights to make them affect differently on the training process of WNN. Besides, the multiscale composite complexity synchronization (MCCS) is used as the new method to evaluate the predictive performance. The empirical experiments are implemented in predicting crude oil prices and moving average absolute return series of WTI and BRE. Through comparing with the traditional back propagation neural network (BPNN), support vector machine (SVM) and WNN models, the empirical results demonstrate that the proposed model has a higher accuracy in crude oil price fluctuations predicting and is advantageous in improving the precision of prediction. (C) 2018 Elsevier Ltd. All rights reserved.